Richard (HoppyUK) reckons...
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My comparison tests of hot-shoe guns' output, though quite extensive and as fair as I can make them, have never been more than 'estimates' of power, or 'equivalents' in terms of Watt-seconds. They put a Canon 580EX at 120Ws, Nissin Di866 at 110Ws and Nikon SB900 at 150Ws.
I use a Lastolite Umbrellabox for this, which is a 100cm reverse-firing white umbrella with softbox front, because it can be fitted to any flash head or gun and it collects 100% of the light and scrambles and projects it in essentially exactly the same way. But I've also got very similar figures using a regular umbrella, white and silver, or a standard double-diffuser softbox - all within 10%. Things would be different with say a strip-box or beauty dish, due to the speedlites' reflector design.
But a Watt-second is a measure of energy stored in the capacitors, not light output, so those numbers can never be more than a rough guide to brightness. However, having tested several dozen different studio heads now, I have a pretty good idea of how Ws generally convert in terms of light, and most of the major brands are broadly similar.
I haven't yet tested the new Lencarta Atoms, but all the evidence suggests they're pretty punchy, and the bare bulb design will help too. And it would be pointless if they were not substantially brighter than any hot-shoe gun as that's what they're about - real portable power.
Personally, I have even less faith in guide numbers than I have in Ws when it comes to comparing real-world total brightness (just too many significant variables in measurement methods) but I'd be surprised if the Atom 180 doesn't have getting on for twice the brightness of the average high-end speedlite, and the 360 maybe four times as much. That's up there with the Elinchrom Quadras.
The other things are the Atoms' recycle times, battery capacity, and ability to keep on working flat-out long after the average speedlite has either over-heated and cut-out, or gone into terminal meltdown.
BTW, Canon manual says 580EX has a guide number of 36 (ISO100/m) with the head set at 35mm*.
*Edit: sorry, Garry wanted 35 degrees not mm, which would be a 58mm lens on full-frame, so between Canon's quoted figures of GN42 at 50mm, and GN50 at 70mm, ie GN45-ish. One stop up on GN45 (x1.4) would be GN63, so in fact if you take those figures as comparable it shows the Atom 180 (GN60) as a bit under one stop brighter than a Canon 580EX - more or less in line with my Ws estimates.